# Tagged Questions

The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

43 views

### Spherical Polar Proof for Non-Commutativity of Indivdual Quantum Angular Momentum Operators

How can the following commutation relation be solved through spherical polar coordinates $[\hat{L}_{z}$,$\hat{L}_{x}]$ = $\imath\hbar\hat{L}_{y}$ I understand the derivation through partial ...
29 views

### Which force acts as centripetal force on gyroscope?

I think I have understood gyroscope in terms of angular momentum and how the torque of gravitational force moves it the way it does. Also I understand the direction in which it would move: What ...
27 views

### Is there a difference between typical spin-spin interaction and Fermi contact interaction from a mathematical point of view?

The reason for this question is that I have a paper that describes some interaction using the Fermi contact interaction in a classical form. I would like to study the same problem using quantum ...
81 views

### Can a spinning object stop spinning?

Suppose there's an object spinning in empty space. That object has mass and angular momentum. Is it possible for that object to stop spinning without any external intervention, say due to a chemical ...
886 views

### Why do we think Spin is angular momentum as opposed to some other quantity? [duplicate]

What leads us to the conclusion that spin is angular momentum? Could it not be some other quantity? Sorry if this is a rookie level question.
78 views

### Angular Momentum of the Dirac field

I'm going through the Peskin & Shroeder's discussion on the Dirac field, and I am struggling with a couple of claims they make about angular momentum. First of all, the angular momentum operator ...
61 views

### How could a heavy manhole cover jump out of the ground, fly through the windshield and hit a driver in a car?

Today (12 of Feb), there was this accident in Boston where a driver was killed because a manhole cover (~200lbs) had somehow become airborne and struck her. The car looks like an SUV, so her head must ...
60 views

### Does a spinning mass follow a straight trajectory in empty space? Or is it curved like a golf ball?

Suppose that we can send to identical satellites (like Voyager 1&2) on identical trajectories. But one spins to the right while the other spins to the left. Would they follow the same ...
36 views

### How to apply torque impulse

In the below question, can we apply conservation of Angular Momentum? If not, why? Moreover how do we apply Torque impulse to the system ? The contact force between the cylinders will be normal to ...
70 views

### Navier Stokes : what about angular momentum?

I play with CFD for a while, and suddenly, a transcendantal question raises: :-) Navier Stokes is basically Newton applied on a continuum in Eulerian. For solids, we would consider linear, but also ...
64 views

### How does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?

So we are looking at central potentials in QM; The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$. We have; ...
2k views

### Do electrons in an atom always have the same 'direction'?

Perhaps speaking of direction of an electron isn't quite correct. But does QM indicates a kind of way whether all electrons are going e.g. 'clockwise' or not? Of course QM just gives a probability ...
307 views

### How can a bowling ball curve in both directions?

There is a popular video on facebook that I just don't understand. A man spins a bowling ball very fast then slightly taps it down the lane. Somehow it does half of a figure eight, curving around two ...
50 views

### Calculating Rolling friction of a car's wheels (NOT ON AN INCLINE)

I'm dealing with a small toy car consisting of a bottle that has a small hole in the back, covered by a thumb tack. The bottle is filled with pressurized air then the thumb tack is released, releasing ...
37 views

### Restriction to the total angular momentum of two identical particles with spin 1

I've been asked if there is any aditional restriction to obtain the possible values of the total angular momentum J by considering that the 2 particles of spin S=1 are identical. If they are not ...
46 views

### Orbital angular momentum eigenstates in the $|\mathbf{r}\rangle$ representation

Consider the orbital angular momentum operators $L^2$ and $L_z$. In the $|\mathbf{r}\rangle$ representation using spherical coordinates those operators actions are given by ...
54 views

### In kerr's black hole solution can the Bekenstein-Hawking entropy be descrete?

In kerr's solution we have: $S_{BH}=\frac{k_{\beta}c^{3}A}{4G\hbar}$ where A is the area of the horizon and equal to $A=8\pi G^2 m(m+\sqrt{m^2 - a^2})$ where $a=\frac{J}{mc}$ and J is the angular ...
87 views

### Angular Momentum Addition in Phase Space QM

In my very limited understanding of geometric quantization, we quantize spin by choosing as our phase space $S^2$ with a suitably normalized area form as the symplectic form. Depending on the ...
88 views

### Adding cinnamon to my coffee makes it stop whirling much faster: Why is thats?

When I stir my coffee in a cup, the fluid spins a long time, but when I pour cinnamon into the cup, the spinning fluid slows and stops very rapidly - why?
62 views

### Measuring Rotation of Sun

If the sun had a uniform surface (i.e., if there were no sunspots to look at), is there a practical way to measure its rotation? In other words, if some external force flipped the sun's spin ...
48 views

### How to show the finite rotation of a spin-1/2 system?

I'm reviewing my quantum mechanics by going through Sakurai and Napolitano again and working out all of the derivations. I'm stumped (though I probably shouldn't be) on some algebra in the finite ...
53 views

### What is relationship between linear and angular momentum?

I'm confused about imparting momentum to a sphere, which causes it to rotate without slipping. Does the momentum applied go: only to the rotational motion and the linear is a consequence of the ...
86 views

### How has the world remained in balance?

In the center of our galaxy, there is a Supermassive black hole. We were told in early astronomy units of school that black holes are giant vacuums that will absorb/consume the area around it. My ...
70 views

### Small particle rotating around neutron star

First let me say I have read the article at "users.ictp.it › lns003 › Ruoff › Ruoff.ps.gz" about a small particles orbiting a neutron star and causing excitation of different modes of gravitational ...
52 views

As part of several of my homework problems on the subject, I've had to convert between bases, for instance $|+\mathbf{x}\rangle$ in the $S_z$ basis $\left( \frac{1}{\sqrt{2}}\left( |+\mathbf{z}\rangle ... 1answer 33 views ### Precession on a heavy rod: Angular momentum and torque contradiction Say I got a so massive rod and a relatively light spinning flywheel. Fixing an end on a pivot, and the disk on the other endpoint, as expected, the rod would undergo precession. If we call the plane ... 1answer 38 views ### An impulse is given to a sphere out of the center? I'm wondering what will happen if there is an impulse$J$given to a sphere mass$M$out of its center? I'm sure that it will rotate about the center, but what is its translational motion? It will ... 1answer 80 views ### Conservation of angular momentum of system of two objects This may be a silly question, but I just want to clarify something. Say we have two spinning spheres, each spinning about an axis going through their own center of mass: All of the conservation of ... 2answers 63 views ### Intuitive explanation of rotational inertia with respect to angular momentum I understand that there are proofs (e.g. proof, another proof) of why the angular momentum about two points for an object is the same. However, could someone give an intuitive explanation of why this ... 4answers 126 views ### Spinning disk touches stationary disk [closed] Suppose we have a solid disk of mass$M$and radius$R$that is spinning at an angular velocity of$\omega_0$about an axis going out its cm. It is brought to touch a stationary disk of mass$m$and ... 2answers 72 views ### Two particles have the same linear momentum but their angular momentum differ. Which's harder to stop? Which one is harder to stop, a 2 kg particle moving in a circular path of radius 5 m , with angular velocity of 10 rad/s or a 2 kg particle moving in a circular path of radius 2 m with a angular ... 0answers 24 views ### Conservation of angular momentum in a system under torque Let's say we have a particle$A$like this which is located in the disk$c$. Consider that the particle itself is not moving, but in general it is constrained to the semicircle$d$, in that if it ... 1answer 71 views ### Decomposition of tensor product space into direct sum [closed] Consider a tensor product space of two representations$j = \frac{3}{2}$and$j = 1$. How to show$4 \otimes 3 = 6 \oplus 4 \oplus 2$? 1answer 65 views ### Second Kepler's law implies that constant velocity I was trying deduce that if we suppose that the planet's orbits are circular and de Kepler's secong law is true: A line joining a planet and the Sun sweeps out equal areas during equal intervals of ... 0answers 25 views ### Assigning values of angular momentum transfer How do the shapes of the experimentally measured differential scattering or transfer cross sections help in assigning reliable angular momentum transfer values? 1answer 40 views ### If a system is in a state$L^2 =2 \hbar^2$and$L_x=0$why can't$L_z$be 0? A particle is in a state where$L_x=0$and$L^2 = 2\hbar^2$. This means$l=1$and$m_x = 0$. I will call this state$Y^x_{lm} = Y^x_{10}$I wanted to know what possible values$L_z$could have in ... 0answers 21 views ### Coupling between angular momenta of particles conserve angular momentum of each particle? Suppose there are two particles in angular momentum numbers$j_1$and$j_2$respectively. Suppose there is some interaction that couple together the particles' angular momenta. As there is no external ... 2answers 108 views ### Find the error: If$L_x$and$L_y$are zero, then$L_z$is conserved From Goldstein's Classical Mechanics (2nd ed.), problem 38 of chapter 9 basically says the following: It's been shown that the Poisson bracket of two constants of the motion is also a constant of ... 1answer 42 views ### Conservation of Angular Momentum in Einstein - de Haas effect I am not really sure why the law of conservation of angular momentum should hold true in the Einstein - de Haas effect. Consider the following excerpt about the phenomenon (taken from Magnetism in ... 1answer 124 views ### Why is there no 1/3 spin? [duplicate] Why do no particles have a 1/3 spin? Why are all particles' spin either a half-integer or integer? How would a particle with such a spin behave, as a fermion, boson, or neither? 0answers 86 views ### Angular momentum of the vacuum I'm studying quantum field theory from "An introduction to Quantum field theory" by Peskin and Schroeder and from "A modern introduction to quantum field theory" by Maggiore. I've read from "An ... 2answers 110 views ### Conservation of angular momentum while sitting on a spinning chair Today my friend was sitting on a spinning char. By moving his top part of the body left to right and his bottom part of the body the opposite he managed to spin. As I understand Conservation of ... 1answer 23 views ### If$z_G$is a principal axis that goes through the center of mass, are every other axes$z$parralel to$z_G$also principal axes? I know that : If$y$is a principal axis$\iff$you can express the angular momentum with respect to a point$Y$on that axis (if the solid is rotating around that axis of course) with the formula : ... 1answer 100 views ### Conservation of angular momentum during rolling A disk having initial angular velocity$\omega$is gently placed on a rough horizontal surface. What is the angular velocity of rotation when pure rolling starts? I've tried applying conservation ... 2answers 113 views ### Radial quantum number for infinite circular well For completeness, I will sketch the solution of a particle in an infinite circular well first and then get to my question. I apologize in advance since the introduction is standard undergraduate ... 1answer 48 views ### Finding the proportionality constant of the Quantum Angular Momentum raising operator$T_{+}\$ [closed]

This is a question about the mathematics of angular momentum operators in Quantum Mechanics- specifically a recursive relation from Robert Cahn's Semi-Simple Lie Algebras and their Representations ...
90 views

### Gyroscope precession

I have a system diagrammed and explained in the image below. Experimentally I believe the wheel will rotate around the pivot point where the cable is attached in a counter-clock motion if ...
41 views

### Deriving the equation for Angular Momentum? [duplicate]

The equation for angular momentum is L=mvr in which L is the angular momentum, m is the mass, v is the velocity, r is the radius. How does one derive this equation from the other laws of motion?